Springer Series in Computational Mathematics

Introduction to Shape Optimization

Shape Sensitivity Analysis

Authors: Sokolowski, Jan, Zolesio, Jean-Paul

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About this book

This book is motivated largely by a desire to solve shape optimization prob­ lems that arise in applications, particularly in structural mechanics and in the optimal control of distributed parameter systems. Many such problems can be formulated as the minimization of functionals defined over a class of admissible domains. Shape optimization is quite indispensable in the design and construction of industrial structures. For example, aircraft and spacecraft have to satisfy, at the same time, very strict criteria on mechanical performance while weighing as little as possible. The shape optimization problem for such a structure consists in finding a geometry of the structure which minimizes a given functional (e. g. such as the weight of the structure) and yet simultaneously satisfies specific constraints (like thickness, strain energy, or displacement bounds). The geometry of the structure can be considered as a given domain in the three-dimensional Euclidean space. The domain is an open, bounded set whose topology is given, e. g. it may be simply or doubly connected. The boundary is smooth or piecewise smooth, so boundary value problems that are defined in the domain and associated with the classical partial differential equations of mathematical physics are well posed. In general the cost functional takes the form of an integral over the domain or its boundary where the integrand depends smoothly on the solution of a boundary value problem.

Table of contents (4 chapters)

  • Introduction to shape optimization

    Sokolowski, Jan (et al.)

    Pages 5-12

  • Preliminaries and the material derivative method

    Sokolowski, Jan (et al.)

    Pages 13-116

  • Shape Derivatives for Linear Problems

    Sokolowski, Jan (et al.)

    Pages 117-162

  • Shape Sensitivity Analysis of Variational Inequalities

    Sokolowski, Jan (et al.)

    Pages 163-239

Buy this book

eBook $89.00
price for USA in USD (gross)
  • ISBN 978-3-642-58106-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $119.99
price for USA in USD
  • ISBN 978-3-642-63471-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Introduction to Shape Optimization
Book Subtitle
Shape Sensitivity Analysis
Authors
Series Title
Springer Series in Computational Mathematics
Series Volume
16
Copyright
1992
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-58106-9
DOI
10.1007/978-3-642-58106-9
Softcover ISBN
978-3-642-63471-0
Series ISSN
0179-3632
Edition Number
1
Number of Pages
IV, 250
Topics